Topic F.5-3

Topic F.5-4

This topic contains lessons in which students find equivalent fractions using a variety of representations. In the final lesson, students investigate the size of colored areas compared to the whole and “see” that two or more fractions can be related and name the same amount or same area on a grid.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

Georgia

MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 6/2 (3 wholes is equal to six halves); recognize that 3/1 = 3; locate 4/4 and 1 at the same point of a number line diagram.

1. Given a model of an equivalent fraction and guided practice, the student will create a model of an equivalent fraction with 90% accuracy for five out of seven consecutive sessions.

2. Given a model of a fraction with auditory and visual prompts, the student will create an equivalent that has either less or more parts, demonstrating an understanding of the proportional relationship between the numerator and denominator, with 80% accuracy for five consecutive sessions.

3. Given a model and the corresponding fraction, the student will create an equivalent fraction and write the numerator and denominator of the equivalent with no prompting for five out of six examples in three consecutive sessions.

4. Given pre-teaching and a reference whole, students will create two equivalent fractions and write their values with 80% accuracy for three consecutive sessions.

This topic contains lessons in which the student uses the number line to discover that different fraction numbers can represent the same point on the line. In other lessons, the student selects the appropriate sign (<, >, or =) to indicate the relationship between two models or fraction numbers.

Common Core

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Georgia

MGSE4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.

1. Given two fraction models and direct instruction, the student will use the symbols <, >, or = to show the relationship between the two model for five out of six examples in five consecutive trials.

2. Given a number line with tic marks and fraction numbers as visual cues, the student will mark or place up to five fractions in the correct location on the number line with 90% accuracy for three consecutive sessions.

3. Given two fraction numbers and a cognitive strategy, the student will use the symbols <, >, or = to show the relationship between the two model for five out of six examples in five consecutive trials.

This topic introduces students to the procedure for finding equivalent fractions. Initial lessons make the proportional relationship between equivalent fractions more explicit by requiring students to complete a sentence describing the relationship between the two factions. Students work with numbers only in the final lesson.

Common Core

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Georgia

MGSE4.NF.1 Explain why two or more fractions are equivalent a/b = (n × a)/(n × b) ex: ¼ = (3 x 1)/(3 x 4) by using visual fraction models. Focus attention on how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

1. Given two fractions that are equivalent and a prompt, the student will enter in the numbers to complete a sentence describing the relationship between the equivalent fractions for five out of six examples in three consecutive sessions.

2. Given two related fractions with models and a partially completed procedure, the student will enter the “one” fraction to change one fraction and model to an equivalent with a common denominator for five out of six examples on for three consecutive sessions by the end of the first progress-reporting period.

3. Given a fraction and pre-teaching with and without models, the student will independently find at least one equivalent fraction for nine out of ten examples on five consecutive sessions.

Lessons in this topic expand on previous conceptual understanding of equivalence by requiring the student to find two equivalent fractions for the given. Lessons begin with the use of models and fade to numbers only.

Common Core

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Georgia

MGSE4.NF.1 Explain why two or more fractions are equivalent a/b = (n × a)/(n × b) ex: ¼ = (3 x 1)/(3 x 4) by using visual fraction models. Focus attention on how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

1. Given a fraction and two blank models, the student will make models for two equivalents and write the fraction number for five out of six examples in three consecutive sessions.

2. Given a fraction and no more than one verbal prompt, the students will explain and complete the procedure using the “one” fraction to find two equivalent fractions for the given with 80% accuracy by the end of the second marking period.

Equivalent fractions name the same amount by using different-sized fractional parts.

This Big Idea focuses on developing a conceptual understanding of equivalence and the procedure for finding an equivalent for a given fraction. Students develop the understanding that any given fraction can be represented numerous ways but to be equivalent they must have the same value.

Common Core

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Georgia

MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 6/2 (3 wholes is equal to six halves); recognize that 3/1 = 3; locate 4/4 and 1 at the same point of a number line diagram.

MGSE4.NF.1 Explain why two or more fractions are equivalent a/b = (n × a)/(n × b) ex: ¼ = (3 x 1)/(3 x 4) by using visual fraction models. Focus attention on how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

MGSE4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.